When I was growing up and we had chickens (~25 - 30 of the blasted, mean, hand pecking things. I was the egg poacher.) we never washed them. We did not store them ALL that long, because we used so many, but we never had a problem when one got left in the bottom of the bowl for an extra amount of time. Yes, I was supposed to carefully take out the older eggs, put in the new, and add the older ones on top. But I was six. Sometimes I 'forgot'.
Just my opinion.